The class of discrete probabilistic distributions of the II type of a random set on a set of N events is investigated. For constructing such probabilistic distributions, a recurrent formula and associative functions are offered to use. The advantage of the approach is that for the definition of the probabilistic distribution, instead of 2 N probabilities of events, it is enough to know N probabilities and the type of the associative function. This approach is tested for some three associative functions. The theorems establishing their forms and the legitimacy conditions for obtained probabilistic distributions of random sets of events are proven.
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- Title Recurrent formation of discrete probabilistic distributions of random sets of events
- Headline Recurrent formation of discrete probabilistic distributions of random sets of events
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Tomsk State University - Issue Prikladnaya Diskretnaya Matematika - Applied Discrete Mathematics 4(26)
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Keywords
associative function, random set of events, discrete probability distributions, ассоциативная функция, дискретное вероятностное распределение, случайное множество событийAuthors
References
Goldenok E. E., Lukyanova N. A., and Semenova D. V. Applications of wide dependence theory in eventological scoring // Proc. IASTED Intern. Conf. Automation Control and Inform. Technology, Control, Diagnostics, and Automation. Novosibirsk: ACTA Press Anaheim|Calgary|Zurich, 2010. P. 316-322.
Logical, Algebraic, Analytic, and Probabilistic Aspects of Triangular Norms / eds. E. P. Klement and R. Mesiar. Amsterdam: Elsevier, 2005. 481 p.
Орлов А. И. Нечисловая статистика. М.: МЗ-Пресс, 2004. 513 с.
Klement E. P., MesiarR., and Pap E. Triangular Norms. Boston: Kluwer Academic Pub., 2000. 220 p.
Schweizer B. and Sklar A. Probabilistic Metric Spaces. N.Y.: North Holland, 1983. 275 p.
Nelsen R. B. An Introduction to Copulas (second edition). N.Y.: Springer Science+Business Media, Inc., 2006. 270p.
MengerK. Statistical metrics // Proc. Nat. Acad. Sci. USA. 1942. No. 8. P. 535-537.
Semenova D. V. and Lukyanova N. A. Random set decomposition of joint distribution of random variables of mixed type // Proc. IAM. 2012. V. 1. No. 2. P. 50-60.
Semenova D. V. and Shangareeva L. Yu. Associative Ali-Mikhail-Haq's random set // Proc. scientific-applied conf. «Statistics and its Applications». Tashkent: National University of Uzbekistan, 2013. P. 88-94.
Alsina S., Frank M, and Schveizer B. Associative Functions: Triangular Norms and Copulas. Singapore: World Scientific Publishing Co. Pte. Ltd., 2006. 237p.
Semenova D. V. On new notion of quasi-entropies of eventological distribution // Proc. Second IASTED Intern. Multi-Conf. Automation Control and Inform. Technology. Novosibirsk: ACTA PRESS, 2005. P. 380-385.
Vorobyev O. Yu. and Lukyanova N. A. Properties of the entropy of multiplicative-truncated approximations of eventological distributions //J. Siberian Federal University. Math. & Physics. 2011. V.4. No. 1. P. 50-60.
Воробьев О. Ю., Воробьев А. О. Суммирование сет-аддитивных функций и формула обращения Мебиуса // Доклады РАН. 2009. Т. 336. №4. С. 417-420.
Ширяев А. Н. Вероятность-1. М.: МЦНМО, 2004. 519с.
Nguyen H. T. An Introduction to Random Sets. Boca Raton: Taylor & Francis Group, LLC, 2006. 240 p.
Recurrent formation of discrete probabilistic distributions of random sets of events | Prikladnaya Diskretnaya Matematika - Applied Discrete Mathematics. 2014. № 4(26).
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